PARIS (Reuters) - The BPI France public investment bank aims to invest about one billion euros ($1.37 billion) in a large or mid-sized company, and could consider investing in the upcoming spin-off of Euronext, its head said on Friday.

The operation, which could come this year if the right opportunity arose, would be part of the 1-2 billion euros the BPI has earmarked for capital investments in French companies each year.

"We would like to make a billion-euro investment in a major deal," BPI managing director Nicolas Dufourcq said, presenting the BPI's annual results.

Dufourcq said that one deal the BPI would look at was the spin-off of the Euronext stock market operator from the New York Stock Exchange.

"Whether it's the (state-owned) Caisse des Depots et Consignations (CDC) that invests in Euronext, or us, or nobody, that remains to be seen," he said.

Eager for the stock market operator to be in French hands, the government and regulators have for months been pushing banks and insurers to take a large stake in Euronext, but they have shown little enthusiasm for the idea.

The BPI, which is half owned by the French state and half by the CDC, was set up last year to help provide funding mainly for credit-starved small and mid-sized companies to make investments.

Speaking at the presentation, Finance Minister Pierre Moscovici said the BPI also "has a role to play in big companies to help keep their shareholder structures stable". ($1 = 0.7317 euros)